Mechanical stability of the CO 2 −CH 4 heteroclathrate hydrate dominates the geomechanical stability of natural gas hydrate deposits when CO 2 replaces CH 4 from gas hydrate reservoirs. Here, molecular dynamics simulations were employed to investigate the strain-induced fracture behaviors of the CO 2 − CH 4 heteroclathrate hydrate under mechanical loadings at various temperatures, pressures, and CO 2 saturations. Results show that all crystals exhibit brittle fracture behavior, and a crack first develops in the location where hydrogen bonds (HBs) in the hexagonal rings of the large 5 12 6 2 cages are parallel to the tensile direction. Increasing the temperature or CO 2 saturation leads to the decrease in Young's modulus and fracture strength of the CO 2 −CH 4 heteroclathrate hydrate. Particularly, abnormal mechanical strengthening of hydrates is observed when the CO 2 saturation is around 0.75, mainly attributed to the coupling of the lattice distortion with the host−guest interaction. HBs are the key factors to dominate the deformation of the CO 2 −CH 4 heteroclathrate hydrate. The slow decrease, rapid decrease, and abrupt increase in HB dynamics are corresponding to the elastic deformation, elastic−plastic deformation, and brittle fracture of the CO 2 −CH 4 heteroclathrate hydrate, respectively. With the further stretching after the brittle fracture, the water bridge made up of water molecules released by broken cages at high temperatures leads to different plasticity than at low temperatures and causes a further reduction of HBs. This work advances the understanding of mechanical stability of the gas hydrate, which is believed to be useful in the risk assessment of CO 2 replacing CH 4 from natural gas hydrates and the storage of CO 2 in gas hydrate reservoirs.

With the ensemble Kalman filter (EnKF) or smoother (EnKS), it is easy to adjust a wide variety of model parameters by assimilation of dynamic data. We focus on the case where reallizations and estimates of the depths of the initial fluid contacts as well as gridblock rock property fields are generated by matching production data with the EnKS. The objective is to account for uncertainty in the depths of the contacts and provide improved estimates of the depths by conditioning reservoir models to production data. The efficiency of EnKF and EnKS arises because data are assimilated sequentially in time and so "history matching data" requires only one forward run of the reservoir simulator for each ensemble member. For EnKS and EnKF to yield reliable characterizations of the uncertainty in model parameters and future performance predictions, the updated reservoir simulation variables, e.g., saturations and pressures, must be statistically consistent with the realizations of these variables that would be obtained by rerunning the simulator from time zero using the updated model parameters. This statistical consistency can only be established under assumptions of Gaussianity and linearity that do not normally hold. Here, we explore the use of iterative EnKS methods that are statistically consistent to improve the performance of EnKS. Introduction Since the ensemble Kalman filter (EnKF) was introduced by Evensen (1994) in the context of ocean dynamics literature as a Monte Carlo approximation of the extended Kalman filter, it has been used extensively in meteorological and oceanographical systems. Since its introduction into the petroleum engineering literature (Naevdal et al., 2003, 2003), it has been the subject of extensive research investigation in petroleum engineering as summarized recently by Aanonsen et al. (2008). Moreover, it is now been applied successfully to several field cases (Haugen et al., 2006; Evensen et al., 2007; Bianco et al., 2007) in the sense that application of the EnKF improved the history matches obtained by more traditional methods. A comprehensive overview of the methodology and theory can be found in Evensen (2007). One of the strengths of EnKF is the fact that one can easily incorporate virtually any model parameters into the state vector and subsequently adjust these parameters by assimilating production and seismic data. In the field example presented by Evensen et al. (2007), and in the problem considered here, the set of model parameters include the depths of the initial fluid contacts as well as gridblock porosities and permeabilities. As the initial depths of contacts are adjusted at every data assimilation step, the method is an emsemble Kalman smoother (EnKS) even though we do not explicitly update the initial saturation and pressure distributions during data assimilation. The basic problem of updating depths of initial fluid contacts was considered previously by Thulin et al. (2007). The data matches and uncertainty estimates they obtained using EnKF (EnKS) were not nearly as good as expected. As we discuss in more detail later, one reason for that is that they used in inappropriate truncation scheme in singular value decomposition (SVD). Results presented here indicate that a second reason for the relatively poor performance is due to nonlinearity.

With the ensemble Kalman filter (EnKF) or smoother (EnKS), it is easy to adjust a wide variety of model parameters by assimilation of dynamic data. We focus first on the case where realizations and estimates of the depths of the initial fluid contacts, as well as gridblock rock-property fields, are generated by matching production data with the EnKS. Then we add the parameters defining power law relative permeability curves to the set of parameters estimated by assimilating production data with EnKS. The efficiency of EnKF and EnKS arises because data are assimilated sequentially in time and so "history matching data" requires only one forward run of the reservoir simulator for each ensemble member. For EnKS and EnKF to yield reliable characterizations of the uncertainty in model parameters and future performance predictions, the updated reservoir-simulation variables (e.g., saturations and pressures) must be statistically consistent with the realizations of these variables that would be obtained by rerunning the simulator from time zero using the updated model parameters. This statistical consistency can be established only under assumptions of Gaussianity and linearity that do not normally hold. Here, we use iterative EnKS methods that are statistically consistent, and show that, for the problems considered here, iteration significantly improves the performance of EnKS.

This paper proposes an augmented Lagrangian method for production optimization in which the cost function to be maximized is defined as an augmented Lagrangian function consisting of the net present value (NPV) and all the equality and inequality constraints except the bound constraints. The bound constraints are dealt with using a trustregion gradient projection method. The paper also presents a way to eliminate the need to convert the inequality constraints to equality constraints with slack variables in the augmented Lagrangian function, which greatly reduces the size of the optimization problem when the number of inequality constraints is large. The proposed method is tested in the context of closedloop reservoir management benchmark problem based on the Brugge reservoir setup by TNO. In the test, we used the ensemble Kalman filter (EnKF) with covariance localization for data assimilation. Production optimization is done on the updated ensemble mean model from EnKF. The production optimization resulted in a substantial increase in the NPV for the expected reservoir life compared to the base case with reactive control.

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